Building upon recent results obtained in [7,8,9], we describe an efficient second order, A-stable scheme for solving the wave equation, based on the method of lines transpose (MOL T ), and the resulting semi-discrete (i.e. continuous in space) boundary value problem. In [7], A-stable schemes of high order were derived, and in [9] a high order, fast O(N ) spatial solver was derived, which is matrix-free and is based on dimensional-splitting.In this work, are interested in building a wave solver, and our main concern is the development of boundary conditions. We demonstrate all desired boundary conditions for a wave solver, including outflow boundary conditions, in 1D and 2D. The scheme works in a logically Cartesian fashion, and the boundary points are embedded into the regular mesh, without incurring stability restrictions, so that boundary conditions are imposed without any reduction in the order of accuracy. We demonstrate how the embedded boundary approach works in the cases of Dirichlet and Neumann boundary conditions. Further, we develop outflow and periodic boundary conditions for the MOL T formulation. Our solver is designed to couple with particle codes, and so special attention is also paid to the implementation of point sources, and soft sources which can be used to launch waves into waveguides.
The application of viscous-flow solvers to calculate the forces on ship hulls in oblique motion has been studied for a long time. However, only a few researchers have published work in which the flow around ships in steady turns was studied in detail. To predict ship manoeuvres, an accurate prediction of the loads due to rotational motion is also required. In a collaborative CFD exercise, the Submarine Hydrodynamics Working Group (SHWG) performed calculations on the bare hull DARPA SUBOFF submarine to investigate the capability of RANS viscous-flow solvers to predict the flow field around the hull and the forces and moments for several steady turns. In the study, different commercial as well as bespoke flow solvers were used, combined with different turbulence models and grid topologies. The work is part of a larger study aiming to improve the knowledge and understanding of underwater vehicle hydrodynamics. In this paper, the results of the exercise will be presented. For several cases, verification studies are done to estimate the uncertainties in the results. Flow fields predicted by the different members of the SHWG are compared and the influence of the turbulence model will be discussed. Additionally, the computed forces and moments as a function of the drift angle during the steady turns will be validated. It will be demonstrated that using sufficiently fine grids and advanced turbulence models without the use of wall functions will lead to accurate prediction of both the flow field and loads on the hull.
When a periodic waveform with a discrete-harmonic spectrum is temporally windowed to make a signal, its spectrum becomes a continuous function of frequency. However, there are discrete-frequency representations for windowed signals such as the Fourier series representation of a periodically extended signal. This article introduces the concept of matching between the temporal window and the periodic waveform. Matching leads to a discrete-frequency representation in which the Fourier transform of the windowed signal preserves the amplitudes and phases of the waveform on the set of original waveform frequencies. Generating signals with matched window and waveform leads to important control of experiments.
We propose a new particle-in-cell (PIC) method for the simulation of plasmas based on a recently developed, unconditionally stable solver for the wave equation. This method is not subject to a CFL restriction, limiting the ratio of the time step size to the spatial step size, typical of explicit methods, while maintaining computational cost and code complexity comparable to such explicit schemes. We describe the implementation in one and two dimensions for both electrostatic and electromagnetic cases, and present the results of several standard test problems, showing good agreement with theory with time step sizes much larger than allowed by typical CFL restrictions.
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